Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
//package com.company;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.net.Inet4Address;
import java.time.temporal.ChronoUnit;
import java.util.*;
public class Main implements Runnable {
    static boolean v[];
    static int ans[];
    int size[];
    static int count = 0;
    static int dsu = 0;
    static int c = 0;
    static int e9 = 1000000007;
    int min = 0;
    int max = Integer.MIN_VALUE;
    long max1 = Long.MIN_VALUE;
    long min1 = Long.MAX_VALUE;
    boolean aBoolean = true;
    boolean y = false;
    long m = 0;
    static boolean t1 = false;
    long fib[][];
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    int parent[];
    int rank[];
    int n = 0;
    ArrayList<ArrayList<Edge>> arrayLists;
    boolean v1[];
    static boolean t2 = false;
    boolean r = false;
    int min3 = Integer.MAX_VALUE;
    int k = 0;
    Queue<Long> queue;
    long p = 0;
    long fib1[][];
    int dp[][];
    public static void main(String[] args) throws IOException {
        new Thread(null,new Main(),"Main",1<<28).start();
    }

    public void run(){
        FastReader scanner = new FastReader();
//            Scanner scanner = new Scanner(System.in);
//            BufferedReader bufferedReader=new BufferedReader(new InputStreamReader(System.in));
//            String s;
        PrintWriter printWriter = new PrintWriter(System.out);
        long t=1;
        while (t-->0) {
            int n=scanner.nextInt();
            int arr[]=new int[n];
            int o=0;
            int ans=0;
            boolean r=false;
            for (int i = 0; i < n; i++) {
                int a=scanner.nextInt();
                arr[i]=a;
                if(a%2!=0){
                    r=true;
                    o=i+1;
                }
                ans+=a;
            }
            dp=new int[n+1][ans+1];
            if(ans%2!=0){
                printWriter.println(0);
                printWriter.flush();
                return;
            }
            boolean r1=find(arr,n,ans/2);
            if(!r1){
                printWriter.println(0);
            }
            else{
                if(r){
                    printWriter.println(1);
                    printWriter.println(o);
                }else{
                    while(!r){
                        for (int i = 0; i < n; i++) {
                            arr[i]=arr[i]/2;
                            if(arr[i]%2!=0){
                                r=true;
                                o=i+1;
                                break;
                            }
                        }
                    }
                    printWriter.println(1);
                    printWriter.println(o);
                }
            }
        }
        printWriter.flush();
    }

    static final int mod=1_000_000_007;
    public boolean find(int arr[],int n,int ans){
        if(dp[n][ans]!=0){
            return dp[n][ans]==1?false:true;
        }
        if(ans==0){
            return true;
        }
        if(n==0&&ans!=0){
            return false;
        }
        if(arr[n-1]>ans){
            return find(arr,n-1,ans);
        }
        boolean r=find(arr,n-1,ans-arr[n-1])||find(arr,n-1,ans);
        if(r){
            dp[n-1][ans]=2;
        }else{
            dp[n-1][ans]=1;
        }
        return r;
    }
    public long mul(long a, long b) {
        return a*b%mod;
    }
    public long fact(int x) {
        long ans=1;
        for (int i=2; i<=x; i++) ans=mul(ans, i);
        return ans;
    }
    public long fastPow(long base, long exp) {
        if (exp==0) return 1;
        long half=fastPow(base, exp/2);
        if (exp%2==0) return mul(half, half);
        return mul(half, mul(half, base));
    }
    public long modInv(long x) {
        return fastPow(x, mod-2);
    }
    public long nCk(int n, int k) {
        return mul(fact(n), mul(modInv(fact(k)), modInv(fact(n-k))));
    }
    public void parent(int n){
        parent=new int[n+1];
        size=new int[n+1];
        rank=new int[n+1];
        for (int i = 0; i <=n; i++) {
            parent[i]=i;
            rank[i]=0;
            size[i]=1;
        }
    }
    public void union(int i,int j){
        p--;
        int root1=find(i);
        int root2=find(j);
//            if(root1 != root2) {
//                parent[root2] = root1;
////                sz[a] += sz[b];
//            }
        if(root1==root2){
            return;
        }
        if(rank[root1]>rank[root2]){
            parent[root2]=root1;
            size[root1]+=size[root2];
        }
        else if(rank[root1]<rank[root2]){
            parent[root1]=root2;
            size[root2]+=size[root1];
        }
        else{
            parent[root2]=root1;
            rank[root1]+=1;
            size[root1]+=size[root2];
        }
    }
    public int find(int p){
        if(parent[p]!=p){
            if(parent[p]==-1){
                return parent[p];
            }
            parent[p]=find(parent[p]);
        }
        return parent[p];
    }
    public double dist(double x1,double y1,double x2,double y2){
        double e=(x2-x1)*(x2-x1)+(y2-y1)*(y2-y1);
        double e1=Math.sqrt(e);
        return e1;
    }
    public void make(int p){
        parent[p]=p;
        rank[p]=1;
    }
    Random rand = new Random();
    public void sort(int[] a, int n) {
        for (int i = 0; i < n; i++) {
            int j = rand.nextInt(i + 1);
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
        Arrays.sort(a, 0, n);
    }
    public long gcd(long a,long b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }
    //    public void dfs(ArrayList<Integer> arrayList){
//        for (int i = 0; i < arrayList.size(); i++) {
//            if(v1[arrayList.get(i)]==false){
//                v1[arrayList.get(i)]=true;
//                dfs(arrayLists.get(i));
//            }
//        }
//    }
    public double fact(double h){
        double sum=1;
        while(h>=1){
            sum=(sum%e9)*(h%e9);
            h--;
        }
        return sum%e9;
    }
    public long primef(double r){
        long c=0;
        long ans=1;
        while(r%2==0){
            c++;
            r=r/2;
        }
        if(c>0){
            ans*=2;
        }
        c=0;
//            System.out.println(ans+" "+r);
        for (int i = 3; i <=Math.sqrt(r) ;i+=2) {
            while(r%i==0){
//                    System.out.println(i);
                c++;
                r=r/i;
            }
            if(c>0){
                ans*=i;
            }
            c=0;
        }
        if(r>2){
            ans*=r;
        }
        return ans;
    }
    public long divisor(double r){
        long c=0;
        for (int i = 1; i <=Math.sqrt(r); i++) {
            if(r%i==0){
                if(r/i==i){
                    c++;
                }
                else{
                    c+=2;
                }
            }
        }
        return c;
    }
}
class Pair {
    long x;
    int y;
    int z;
    public Pair(long x,int y,int z) {
        this.x = x;
        this.y = y;
        this.z=z;
    }

    // @Override
//    public int hashCode() {
//        int hash = 37;
//        return this.x * hash + this.y;
//    }
//
//    @Override
//    public boolean equals(Object o1) {
//        if (o1 == null || o1.getClass() != this.getClass()) {
//            return false;
//        }
//        Pair o = (Pair) o1;
//        if (o.x == this.x && o.y == this.y) {
//            return true;
//        }
//        return false;
//    }
}
class Sorting implements Comparator<Pair> {
    public int compare(Pair p1, Pair p2) {
//        if(p1.y==p2.y){
//            return Long.compare(p1.x,p2.x);
//        }else {
        return Long.compare(p1.x, p2.x);
        // }
    }
}
class Edge{
    int s=0;
    int d=0;
    int c=0;
    public Edge(int s,int d,int c){
        this.s=s;
        this.d=d;
        this.c=c;
    }
}